The six key parts of PLT Redex are
language, reduction-relation,
define-metafunction,
stepper, redex-check, and test-->. There are
many other functions in the library that build on these
(and provide variations and extensions), but these
illustrate the key services that PLT Redex provides.
The first,

(define-language name
(non-terminal-name rhs-pattern ...)
...)

specifies a BNF grammar for a regular tree language. Each right-hand
side is written in PLT Redex's pattern language (consisting of a
mixture of concrete syntax elements and non-terminals, roughly
speaking). With a language definition in place, the
reduction-relation form
is used to define the reduction relation:

(reduction-relation language-name
(--> lhs-pattern consequence) ...)

Syntactically, it consists of three sub-expressions: a language to
which the reduction applies, a source pattern specifying which terms
the rule matches, and Racket code that, when evaluated, produces the
resulting term as an S-expression.
Metafunctions are defined like this:

The define-metafunction form defines the
metafunction name by cases. Unlike the reduction relation, the
branches for a metafunction are ordered. As soon as one of
the patterns matches, that branch is taken regardless of
other matches that might happen.
The functions

open GUI windows that let you explore the reduction graph of
terms reachable from the initial
term. The stepper behaves in a manner similar
to DrRacket's stepper, and traces shows the
reduction graph in a graph-viewing window.
Redex can randomly generate example expressions to try to falsify
conjectures about the rewriting system. For example, this expression

(redex-check language-name pattern predicate)

randomly generates expressions matching
pattern (typically a non-terminal)
from the language language-name and then evaluates
predicate. If it ever returns false,
redex-check reports the expression that
falsified the predicate.
Finally,

(test--> reduction-relation starting-term final-terms ...)

can be used to develop test
suites for PLT Redex programs. It accepts a reduction
relation and an example term and applies the reduction
relation until it cannot reduce any further, at which point
it checks to make sure that each the given final terms
match.